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Isometries of Hp(Un)

Published online by Cambridge University Press:  20 November 2018

R. B. Schneider
R. B. Schneider*
Affiliation:
Cornell University, Ithaca, New York
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Forelli in [1] has described the isometries of Hp(U) into Hp(U) for p≠2, 0 < p < ∞. We shall extend his methods to characterize the isometries of Hp(Un) onto Hp(Un).

The notation we shall use can be found in Rudin [3].

Let II represent a permutation that induces a map on functions of n complex variables by

Clearly II is an isometry of Hp(Un) onto Hp(Un).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 1 , February 1973 , pp. 92 - 95
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Frank, Forelli, The isometries of Hpt Can. J. Math. 16 (1964), 721–728.Google Scholar
2. Robert, Gunning and Hugo, Rossi, Analytic functions of several complex variables (Prentice Hall, New York, 1965).Google Scholar
3. Walter, Rudin, Function theory on polydiscs (Benjamin, New York, 1969).Google Scholar